6 Responses to “4D Pong, continued”

Well, I tried, but I don’t know what I’m looking at, and I don’t know how to tell when I’ve actually hit the puck vs. it just bouncing off a wall. I don’t think I get the shape of the hyperspace. How should I think about it?

BTW, are you left-handed? Just wondering based on the choice of control keys. I have a much easier time using my right hand for the left-right/up-down.

The hypercube exists in four dimensions — x,y,z,w. Since it’s a hypercube, it has eight hyperfaces, each of which is a cube. Every time the puck hits and bounces off a hyperface, that hyperface lights up (you see its edges glow).

Six of the hyperfaces are in the positive and negative x, y, and z dimensions. When the puck hits one of these hyperfaces, that hyperface glows white. Essentially, these six hyperfaces are the walls that the puck can bounce off on its way from one end of the playing field to the other.

The two hyperfaces in the positive and negative w dimension are special. They are the near (red) and far (blue) hyperfaces. You are hitting the puck from the red toward the blue, and your opponent is hitting the puck from the blue toward the red. Your job is to move your red paddle in x,y,z to block the opponent’s shot.

That explanation is very helpful. I’m starting to get a better mental model of this. (Higher-dimensional geometries are not something I’ve spent much time thinking about). I was also looking at the pictures on this Wikipedia page: http://en.wikipedia.org/wiki/Tesseract. Which of the faces in your 4d hypercube are solid and which can the puck pass through? (I hope that question makes sense.)

Sharon, here is what makes it tricky. The faces on the 4D hypercube have volume, but they don’t have hypervolume (the 4D equivalent of volume). The puck lives in the hypervolumetric interior of the hypercube. It bounces off the walls (those eight hyperfaces) and then careens off into another direction inside the hypervolume.

It starts to make more sense if you think about the 3D equivalent of this situation: a ball bouncing around in a 3D cube. The square faces of the cube have area, but they don’t have volume. If a ball lives in the volumetric interior of a cube, it will bounce off the cube’s six walls, and then careen off into another direction inside the cube.

What’s tricky and interesting in the 4D pong game is that from the point of view of the puck — which is a four dimensional object — the cubic hyperfaces of the playing area are “flat” — they don’t have any 4D hypervolume, so the puck cannot live in them, it can only bounce off of them.

I wonder if there is a “games for learning” opportunity here. Could you create the game in such a way that it progresses from 2d pong to 4d pong and, in the process, teaches the player about 4d hypercubes?